For most individuals, the use made of health care in a given year is determined principally by unpredictable random incidents. Of course, some individuals have a predictably higher predisposition to illness than others. However, the general consensus is that only a fraction of individual variability in health care costs can be predicted. The purpose of this paper is to explore the implications of this inherent randomness for setting health care budgets for general practitioner purchasers of health care. The paper argues that variability in utilization in health care is very high; that no capitation formula can ever completely capture that variability, even for large populations; that the variability may give rise to certain dysfunctional consequences if not managed carefully; and that therefore careful attention should be given to the managerial arrangements associated with any devolution of health care budgets.